An interference pattern is produced when two coherent beams of radiation, both of which may be derived from a common source, travel through different paths to a surface at which the beams interfere with each other. The resulting interference pattern can be analyzed to measure parameters such as phase difference between the two interfering beams.
An interferometer is an instrument comprising components defining different paths for beams derived from a common radiation source, and a means for detecting the interference pattern produced at the surface where the beams interfere. Major causes of measurement error in analyzing interference patterns include instability of the radiation source, noise generated by the detector means, dynamic range limitations of the detector means, atmospheric turbulence, and systematic errors inherent in the interferometer.
Phase-shifting interferometers and heterodyne interferometers have been used in the prior art for measuring the phase difference between two interfering coherent beams. A phase-shifting interferometer introduces phase modulation into one of the interfering beams, and typically uses an electronic phase detection technique to determine the phase difference between the interfering beams. A major disadvantage of phase-shifting interferometry is that presently available phase modulation devices generally have limited bandwidth, and therefore cannot be used effectively in applications requiring analysis of short pulses of radiation.
A heterodyne interferometer introduces frequency modulation into one of the two interfering coherent beams, and typically also uses an electronic phase detection technique to determine the phase difference between the interfering beams. In general, the irradiance distribution I at the interference surface (x,y) of any interferometer can be expressed by the equation EQU I(x,y)=I.sub.O (x,y)+I.sub.1 (x,y) cos [.phi.(x,y)], (1)
where I.sub.O is the unmodulated (DC) component of the irradiance, I.sub.1 is the amplitude of the modulated (AC) component of the irradiance, and .phi.(x,y) is the spatial phase difference between the two interfering beams. In heterodyne interferometry, a temporal phase modulation .phi.(t) is introduced into one of the two interfering beams so as to produce a time-dependent irradiance expressed as EQU I(x,y,t)=I.sub.O (x,y)+I.sub.1 (x,y) cos [.phi.(x,y)+.phi.(t)]. (2)
The irradiance distribution I can be measured by, e.g., a two-dimensional array of photodetector elements positioned at the interference surface, and the spatial phase difference .phi.(x,y) can be extracted from the time-varying signal [.phi.(x,y)+.phi.(t)]. The speed with which a heterodyne interferometer can resolve the spatial phase difference .phi.(x,y) depends upon the bandwidth of the temporal phase modulation .phi.(t).